Asymptotic analysis of the steady advection-diffusion problem in axial domains

• Autorzy: Morales Fernando A.

Identyfikatory

DOI

10.7494/OpMath.2023.43.2.199

• Języki publikacji: EN

Abstrakty

EN

We present the asymptotic analysis of the steady advection-diffusion equation in a thin tube. The problem is modeled in a mixed-type variational formulation, in order to separate the phenomenon in the axial direction and a transverse one. Such formulation makes visible the natural separation of scales within the problem and permits a successful asymptotic analysis, delivering a limiting form, free from the initial geometric singularity and suitable for approximating the original one. Furthermore, it is shown that the limiting problem can be simplified to a significantly simpler structure.

Słowa kluczowe

EN

asymptotic analysis; mixed-type variational formulations; advection-diffusion

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 2
• Strony: 199--220
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Morales Fernando A.

• Universidad Nacional de Colombia, Sede Medellín, Escuela de Matemáticas, Carrera 65 # 59A–110, Bloque 43, of 106, Medellín – Colombia

• https://orcid.org/0000-0002-5691-1247

Bibliografia

• [1] J. Auriault, P. Adler, Taylor dispersion in porous media: Analysis by multiple scale expansions, Advances in Water Resources 18 (1995), no. 4, 217–226.
• [2] J.-L. Auriault, C. Geindreau, C. Boutin, Filtration law in porous media with poor separation of scales, Transport in Porous Media 60 (2005), no. 1, 89–108.
• [3] F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
• [4] K.D. Cherednichenko, V.P. Smyshlyaev, On full two-scale expansion of the solutions of nonlinear periodic rapidly oscillating problems and higher-order homogenised variational problems, Archive for Rational Mechanics and Analysis 174 (2004), no. 3, 385–442.
• [5] A. Fiori, I. Jankovic, On preferential flow, channeling and connectivity in heterogeneous porous formations, Mathematical Geosciences 44 (2012), no. 2, 133–145.
• [6] G. Gatica, A Simple Introduction to the Mixed Finite Element Method: Theory and Applications, SpringerBriefs in Mathematics, Springer International Publishing, 2014.
• [7] U. Hornung, Miscible Displacement, Springer New York, New York, NY, 1997.
• [8] R.G. McLaren, P.A. Forsyth, E.A. Sudicky, J.E. VanderKwaak, F.W. Schwartz, J.H. Kessler, Flow and transport in fractured tuff at Yucca Mountain: numerical experiments on fast preferential flow mechanisms, Journal of Contaminant Hydrology 43 (2000), no. 3, 211–238.
• [9] F.A. Morales, J.M. Ramírez, Tangential fluid flow within 3D narrow fissures: Conservative velocity fields on associated triangulations and transport processes, Mathematical Methods in the Applied Sciences 40 (2017), no. 18, 6316–6331.
• [10] M. Peszyńska, R. Showalter, S.-Y. Yi, Flow and transport when scales are not separated: Numerical analysis and simulations of micro- and macro-models, International Journal of Numerical Analysis and Modeling 12 (2015), no. 3, 476–515.
• [11] J.M. Ramirez, E.A. Thomann, E.C. Waymire, R. Haggerty, B. Wood, A generalized Taylor-Aris formula and skew diffusion, Multiscale Modeling & Simulation 5 (2006), no. 3, 786–801.
• [12] P. Royer, Low scale separation induces modification of apparent solute transport regime in porous media, Mechanics Research Communications 87 (2018), 29–34.
• [13] P. Royer, Advection–diffusion in porous media with low scale separation: Modelling via higher-order asymptotic homogenisation, Transport in Porous Media 128 (2019), no. 2, 511–551.
• [14] A.P.S. Selvadurai, On the advective-diffusive transport in porous media in the presence of time-dependent velocities, Geophysical Research Letters 31 (2004) 13.
• [15] R.E. Showalter, Hilbert Space Methods for Partial Differential Equations, volume 1 of Monographs and Studies in Mathematics, Pitman, London-San Francisco, CA-Melbourne, 1977.
• [16] L. Tartar, Correctors in Linear Homogenization, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.
• [17] S. Wang, Q. Feng, X. Han, A hybrid analytical/numerical model for the characterization of preferential flow path with non-darcy flow, PLOS ONE 8 (2014), no. 12, 1–16.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)